DLMF:16.19.E5 (Q5285)

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DLMF:16.19.E5
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    Statements

    Defining formula
    ϑ ⁢ G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) = G p , q m , n ⁡ ( z ; a 1 - 1 , a 2 , … , a p b 1 , … , b q ) + ( a 1 - 1 ) ⁢ G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) , italic-ϑ Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 1 subscript 𝑎 2 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 subscript 𝑎 1 1 Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle\vartheta{G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}% \atop b_{1},\dots,b_{q}}\right)={G^{m,n}_{p,q}}\left(z;{a_{1}-1,a_{2},\dots,a_% {p}\atop b_{1},\dots,b_{q}}\right)+(a_{1}-1){G^{m,n}_{p,q}}\left(z;{a_{1},% \dots,a_{p}\atop b_{1},\dots,b_{q}}\right),}}
    0 references
    DLMF id
    DLMF:16.19.E5
    0 references
    Symbols used
    Meijer $$G$$ -function
    Defining formula
    G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle{G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(% \NVar{z};{\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}}\right)}}
    xml-id
    C16.S17.E1.m2addec
    0 references
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1ddec
    0 references
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1ddec
    0 references
     
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